Question 155447
{{{(x+h)^2}}} Start with the given expression



{{{(x+h)(x+h)}}} Expand. Remember something like {{{A^2=A*A}}}



Now let's FOIL the expression




Remember, when you FOIL an expression, you follow this procedure:



{{{(highlight(x)+h)(highlight(x)+h)}}} Multiply the <font color="red">F</font>irst terms:{{{(x)*(x)=x^2}}}



{{{(highlight(x)+h)(x+highlight(h))}}} Multiply the <font color="red">O</font>uter terms:{{{(x)*(h)=xh}}}



{{{(x+highlight(h))(highlight(x)+h)}}} Multiply the <font color="red">I</font>nner terms:{{{(h)*(x)=hx}}}



{{{(x+highlight(h))(x+highlight(h))}}} Multiply the <font color="red">L</font>ast terms:{{{(h)*(h)=h^2}}}



{{{x^2+xh+hx+h^2}}} Now collect every term to make a single expression. 



{{{x^2+2xh+h^2}}} Now combine like terms. Note: the only "like" terms are {{{xh}}} and {{{hx}}} (which is just the reverse of the first expression). So this means that {{{xh+hx=xh+xh=2xh}}}



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Answer:


So {{{(x+h)^2}}} foils and simplifies to  {{{x^2+2xh+h^2}}}


In other words, {{{(x+h)^2=x^2+2xh+h^2}}}